Question

3x+5y=9 ;5x+3y=41
linear equation ​

Answer 1

Answer

$\sf \dashrightarrow 3x + 5y = 9 \: \: (i)$

$\sf \dashrightarrow 5x + 3y = 41 \: \: (ii)$

By equation i,

$\sf \dashrightarrow 3x + 5y = 9$

$\sf \dashrightarrow 3x = 9 - 5y$

$\sf \dashrightarrow x = \dfrac{9 - 5y}{3}$

Now, we can find the value of y by second equation.

$\sf \dashrightarrow 5x + 3y = 41$

$\sf \dashrightarrow 5 \bigg( \dfrac{9 - 5y}{3} \bigg) + 3y = 41$

$\sf \dashrightarrow \dfrac{45 - 25y}{3} + 3y = 41$

$\sf \dashrightarrow \dfrac{45 - 25y + 9y}{3} = 41$

$\sf \dashrightarrow \dfrac{45 - 16y}{3} = 41$

$\sf \dashrightarrow 45 - 16y = 41 \times 3$

$\sf \dashrightarrow 45 - 16y = 123$

$\sf \dashrightarrow -16y = 123 - 45$

$\sf \dashrightarrow -16y = 78$

$\sf \dashrightarrow y = \dfrac{78}{-16}$

$\sf \dashrightarrow y = \dfrac{-39}{8}$

Now, we can find the value of x by first equation.

$\sf \dashrightarrow 3x + 5y = 9$

$\sf \dashrightarrow 3x + 5 \bigg( \dfrac{-39}{8} \bigg) = 3$

$\sf \dashrightarrow 3x + \dfrac{-195}{8} = 3$

$\sf \dashrightarrow 3x = 3 - \dfrac{-195}{8}$

$\sf \dashrightarrow 3x = \dfrac{24 + 195}{8}$

$\sf \dashrightarrow 3x = \dfrac{219}{8}$

$\sf \dashrightarrow x = \dfrac{219}{8} \times \dfrac{1}{3}$

$\sf \dashrightarrow x = \dfrac{219}{24}$

$\sf \dashrightarrow x = \dfrac{73}{8}$

Hence, the values of x and y are $\sf \dfrac{73}{8}$ and $\sf \dfrac{-39}{8}$ respectively.